12th-octave temperaments
Template:Fractional-octave navigation 12edo is the predominating tuning system in the world today, so some of the 12th octave temperaments have been known for a very long time.
By far the most notable 12th-octave temperament is compton or aristoxenean, associated with the Pythagorean comma, which sets 3/2 to 7\12. Given that the circle of 12 fifths closing was the basis of music in Europe and independently China, it can be argued that the 12th-octave temperaments are the oldest form of musical tradition in history.
Furthermore, 12th-octave temperaments like compton usually temper other intervals to subsets of 12edo, like 9/8 to 6edo whole tone scale, and 5/4 to 3edo.
Another temperament which was hugely known is atomic, stemming from a comma described as the Kirnberger's atom. 3/2 flattened by 32805/32768, the schisma, is extremely close to 7\12.
For temperament data, see:
- Compton - Compton family
- Atomic - Very high accuracy temperaments
Magnesium (5-limit)
Subgroup: 2.3.5
Comma list: [-157 -24 84⟩
Mapping: [⟨12 2 23], ⟨0 7 2]]